Stochastic processes with an embedded point process and their application to system reliability analysis
In applied probability it is fairly familiar to investigate the temporal behaviour of a certain system considered by means of some appropriately chosen (in general random) embedded epochs. This is the idea of the famous method of an embedded Markov chain due to A.Ya. Khinchin and D.G. Kendall. Furthermore, several well-known classes of stochastic processes such as regenerative, semi-Markov and semi-regenerative processes are bases on the concept of embedded points.
KeywordsPoint Process System Reliability Sojourn Time Ergodic Theorem Marked Point Process
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- Beichelt, F. and P. Franken (1983). Zuverlässigkeit und Instandhaltung. Verlag Technik, Berlin.Google Scholar
- Cohen, J.W. (1976). On regenerative processes in queueing theory. Lect. Notes in Econ. Math. Systems, 121, Springer-Verlag, Berlin/Heidelberg/New York.Google Scholar
- Jansen, U. (1984). Conditional expected sojourn times in insensitive queueing systems.Google Scholar
- Keilson, J. (1974). Monotonicity and convexity in systems survival functions and metabolic disappearance curves. in: Reliability and Biometry, SIAM, Philadelphia.Google Scholar
- König, D., K. Matthes and K. Nawrotzki (1971). Unempfindlichkeitseigenschaften von Bedienungsprozessen. Supplement to B.W.Google Scholar
- Gnedenko, I.N. Kovalenko, Einführung in die Bedienungstheorie. Akademie-Verlag, Berlin.Google Scholar
- Natvig, B. and A. Streller (1984). The steady state behaviour of multistate monotone systems. (to appear in JAP).Google Scholar
- Rolski, T. (1981). Stationary random processes associated with point processes. Lect. Notes in Statistics, 5, Springer-Verlag, New York/Heidelberg/Berlin.Google Scholar